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"The Barkleys of Broadway." MGM/UA. $29.95. Made at MGM in 1949, 10 years after the last of the classic Astaire-Rogers musicals at RKO, this final vehicle for Fred and Ginger suffers from a weak Harry Warren score, gimmicky production numbers, flat direction and a tiresome backstage screenplay by Comden and Green that seems intent on recycling malicious gossip about the stars' breakup as a dance team. But the movie has its moments--notably the nostalgic adagio to George Gershwin's "They Can't Take That Away From Me" (introduced in the 1937 Astaire-Rogers film "Shall We Dance") in which his eagerness to lose himself in their on-stage reunion, and her resistance, assume mythic dimensions. In color. Information: (213) 280-6000. ** 1/2